Accumulation body slope seismic stability analysis method based on improved Newmark method

Abstract

The invention provides an accumulation body side slope seismic stability analysis method based on an improved Newmark method, and relates to the technical field of accumulation body side slope seismic stability analys.The method comprises the steps that if a potential sliding face of a bed rock overlying accumulation body is a linear face, the potential sliding face of the bed rock overlying accumulation body is processed in a conventional mode, and if the potential sliding face of the bed rock overlying accumulation body is a linear face, the potential sliding face of the bed rock overlying accumulation body is processed; if the sliding surface is a nonlinear surface, the sliding surface is equivalent to a linear sliding surface based on an energy principle; dividing the accumulation body into an unsaturated state and a saturated state; respectively calculating critical seismic coefficients corresponding to the accumulation body according to an unsaturated state and a saturated state; by adopting an acceleration time-history rectangular strip division method, carrying out segmented integration on the seismic acceleration time history exceeding the critical seismic coefficient to obtain permanent displacements of the sliding body corresponding to an unsaturated state and a saturated state respectively; analyzing the seismic stability of the accumulation body slope by combining the critical seismic coefficient and the permanent displacement; according to the invention, the earthquake stability of the accumulation body slope under the influence of rainfall before earthquake can be comprehensively and accurately reflected.

Description

Technical Field

[0001] This invention relates to the field of seismic stability analysis technology for embankment slopes, and in particular to a seismic stability analysis method for embankment slopes based on an improved Newmark method. Background Technology

[0002] The Newmark method is a commonly used analytical method in engineering to evaluate the stability of embankment slopes under seismic loading. It assumes the sliding mass to be a rigid-plastic body and integrates the portion exceeding the critical acceleration to calculate the permanent displacement of the sliding mass, thereby determining slope stability. However, existing Newmark methods have significant shortcomings in practical applications: Firstly, they do not fully consider the impact of pre-earthquake rainfall, a key environmental factor, on the water content of the embankment, and fail to distinguish the differences in mechanical properties between unsaturated and saturated soil states. This results in the critical seismic coefficient calculation not being specifically adapted to the actual water content of the soil, limiting accuracy. Secondly, for the common non-linear potential sliding surfaces in bedrock overburden embankments, there is a lack of reasonable equivalent treatment schemes based on energy principles, making it difficult to adapt to the analysis needs of complex sliding surface morphologies. Furthermore, the time history processing method for seismic acceleration exceeding the critical seismic coefficient in the permanent displacement calculation is not precise enough, failing to accurately reflect the sliding response law of the embankment under different water content states. Ultimately, this leads to deviations between the slope stability assessment results and actual engineering conditions, resulting in insufficient reliability. Summary of the Invention

[0003] To address the aforementioned technical problems, the technical solution adopted by this invention is as follows: According to the present application, a seismic stability analysis method for accumulated slopes based on the improved Newmark method is provided, the method comprising the following steps: S100, if the potential sliding surface of the bedrock overlying deposits is a straight surface, then the potential sliding surface of the bedrock overlying deposits is treated in the conventional way; if the sliding surface is not a straight surface, then the sliding surface is equivalent to a straight sliding surface based on the energy principle. S200, based on the impact of pre-earthquake rainfall, divides the deposits into unsaturated and saturated states; S300 calculates the critical seismic coefficients for the accumulation body under unsaturated and saturated conditions respectively. S400 uses the rectangular strip method of acceleration time history to integrate the time history of seismic acceleration exceeding the critical seismic coefficient piecewise to obtain the permanent displacement of the sliding body corresponding to the unsaturated state and the saturated state, respectively. S500, combining critical seismic coefficient and permanent displacement, analyzes the seismic stability of the accumulation body slope.

[0004] Furthermore, the method of equating the sliding surface to a straight sliding surface based on the energy principle includes the following steps: S110, determine the initial center of gravity of the sliding body before sliding and the final center of gravity after sliding; S120, combining the horizontal sliding distance of the sliding body and the overall tilt angle before and after sliding, constructs an equivalent straight sliding surface that matches the energy of the actual sliding process.

[0005] Furthermore, in step S300, for the unsaturated state, calculating the critical seismic coefficient corresponding to the accumulation body includes the following steps: S310 defines soil particles with a diameter ≤ 0.075 mm as fine particles, and calculates the fine particle content f. c ; S311, if f c <f thre Then the soil skeleton of the accumulation body is determined to be sand with fine-grained structure; f thre This is the threshold for fine particle content; ; in, =D10 / D50; D10 and D50 are the particle sizes corresponding to 10% and 50% of the sand and fine-grained soil particles, respectively. S312, analyze the normal and tangential forces of the sliding body under seismic load, derive the expression for the relative horizontal acceleration when sliding downhill, set the relative horizontal acceleration of the sliding body = 0, and solve for the critical seismic coefficient of the unsaturated state.

[0006] Furthermore, in step S300, calculating the critical seismic coefficient corresponding to the accumulation body for the saturated state includes the following steps: S320 defines the horizontal length and vertical height of the saturated soil layer, as well as the initial total stress and initial effective stress perpendicular to the sliding surface, and calculates the normal and tangential forces of the saturated soil; where the normal force N s Calculated using the following formula: ; σ n ’ Let L be the initial effective stress perpendicular to the slip surface, L be the horizontal length of the saturated soil layer, and θ be the dip angle of the slip surface. Tangential force T s Calculated using the following formula: ; σ n The initial total stress is perpendicular to the slip surface, and k is the horizontal seismic coefficient; S321, the expression is obtained through force analysis. Substituting the expressions for normal force and tangential force, the critical seismic coefficient for saturation state is obtained after simplification. Among them, the horizontal relative acceleration of the sliding body relative to the bedrock. g is the acceleration due to gravity. , φ The internal friction angle of the soil. φ ∗ The effective internal friction angle is considered after correction of the initial soil stress.

[0007] Furthermore, step S400 includes the following steps: S410, the seismic wave acceleration time history is equivalent to the superposition of constant rectangular blocks with a time increment of Δt, and the acceleration within each block is constant; S420, initial stationary phase, application duration is... constant acceleration kg The integral is obtained t 0 Horizontal relative velocity at time and horizontal relative displacement ; and Satisfy the following formula: ; ; in, t 0 This is the initial time increment.

[0008] S430, subsequent phases ( Using the result of S420 as the initial value, the integral is obtained. t>t 0 horizontal relative velocity at time Relative displacement with respect to the horizontal μ ; ; ; Where t is the cumulative time; S440: Set the velocity of the sliding body to 0 when it stops, substitute the velocity expression to obtain the stopping time, and then substitute the displacement expression to obtain the final relative horizontal displacement in the unsaturated state. ; final relative horizontal displacement under saturation state ; Let be the horizontal relative displacement at time t=t0.

[0009] The present invention has at least the following beneficial effects: The seismic stability analysis method for embankment slopes based on the improved Newmark method of this invention has significant technical advantages: First, based on the energy principle, the non-linear potential slip surface is equivalent to a linear slip surface, effectively solving the problem that existing methods are difficult to adapt to complex slip surface morphologies, and improving the applicability of the Newmark method to embankments with different slip surface types; Second, based on the influence of pre-earthquake rainfall, the method distinguishes between unsaturated and saturated states of the embankment, and calculates the critical seismic coefficient for different states accordingly, making up for the deficiency of existing methods in not considering the differences in soil water content, and significantly improving the calculation accuracy of the critical seismic coefficient; Third, by using the rectangular strip method of acceleration time history to integrate the acceleration time history piecewise beyond the critical seismic coefficient, the permanent displacement of the embankment under different water content states can be accurately calculated, further improving the calculation accuracy of the sliding response parameters; Finally, by combining the critical seismic coefficient and permanent displacement for comprehensive evaluation, the method can comprehensively and accurately reflect the seismic stability of embankment slopes under the influence of pre-earthquake rainfall, providing a more reliable technical basis for the seismic design and risk assessment of embankment slopes in engineering. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 A flowchart of a method for seismic stability analysis of accumulated slopes based on an improved Newmark method provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the force analysis of a rigid slider on an inclined sliding surface under seismic load, provided in an embodiment of the present invention. Figure 3 This is a schematic diagram illustrating the relationship between the acceleration, relative velocity, and relative displacement of the slider and time, as provided in an embodiment of the present invention. Figure 4 This is a schematic diagram of the stress analysis of the saturated soil layer on the sliding surface under seismic load provided in an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the relationship between cumulative strain energy and permanent displacement of a sliding belt, provided in an embodiment of the present invention. Figure 6 This is a schematic diagram of the equivalent slip surface of unsaturated slope failure under seismic loading, provided in an embodiment of the present invention. Figure 7 A schematic diagram of the center of gravity of a loose deposit slope before and after failure, provided in an embodiment of the present invention; Figure 8 This is a schematic diagram of a slope containing a weak interlayer, provided for an embodiment of the present invention. Detailed Implementation

[0012] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0013] It should be noted that, based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Furthermore, this device and / or practice the method can be implemented using other structures and / or functionalities besides one or more of the aspects set forth herein.

[0014] Example 1: The following will refer to Figure 1 The flowchart shown is a method for analyzing the seismic stability of accumulated slopes based on the improved Newmark method, which introduces a method for analyzing the seismic stability of accumulated slopes based on the improved Newmark method.

[0015] The seismic stability analysis method for accumulated slopes based on the improved Newmark method includes the following steps: S100, if the potential sliding surface of the bedrock overlying deposit is a straight surface, then the potential sliding surface of the bedrock overlying deposit is treated in the conventional way; if the sliding surface is not a straight surface, then the sliding surface is equivalent to a straight sliding surface based on the energy principle.

[0016] Furthermore, the method of equating the sliding surface to a straight sliding surface based on the energy principle includes the following steps: S110, determine the initial center of gravity of the sliding body before sliding and the final center of gravity after sliding.

[0017] S120, combining the horizontal sliding distance of the sliding body and the overall tilt angle before and after sliding, constructs an equivalent straight sliding surface that matches the energy of the actual sliding process.

[0018] The stability of deposits overlying bedrock often depends on factors such as the shape, slope, and degree of weathering of the contact surface. Potential slip surfaces can be reasonably assumed to be bedding planes or weak surfaces. In stability analysis of earthquake-prone slopes in mountainous areas, the slip surface of steep slopes can usually be approximated as a straight surface. When the slip surface is non-linear, stability analysis can be performed by equivalently replacing the non-linear slip surface with a straight surface based on the energy principle.

[0019] S200 classifies the deposits into unsaturated and saturated states based on the impact of pre-earthquake rainfall.

[0020] The Newmark method assumes the sliding mass to be a rigid-plastic body that does not deform internally, conceptualizing an earthquake landslide as the sliding of a rigid block on an inclined surface when the acceleration exceeds a critical value. In this method, the critical acceleration depends on the surface inclination angle and a safety factor, and the velocity and displacement of the rigid block are obtained as functions of time by continuously integrating the acceleration exceeding the critical value. The Newmark method can still be used when considering the impact of pre-earthquake rainfall on slope stability under earthquake action. In this embodiment, the impact of pre-earthquake rainfall on the slope of the deposited body is divided into two cases: unsaturated and saturated soil layers.

[0021] S300 calculates the critical seismic coefficients for the accumulation body under both unsaturated and saturated conditions.

[0022] Furthermore, in step S300, for the unsaturated state, calculating the critical seismic coefficient corresponding to the accumulation body includes the following steps: S310 defines soil particles with a diameter ≤ 0.075 mm as fine particles, and calculates the fine particle content f. c .

[0023] S311, if f c <f thre Then the soil skeleton of the accumulation body is determined to be sand with fine-grained structure; f thre This is the threshold for fine particle content; ; in, =D10 / D50; D10 and D50 are the particle sizes corresponding to 10% and 50% of the sand and fine-grained soil particles, respectively.

[0024] S312, analyze the normal and tangential forces of the sliding body under seismic load, derive the expression for the relative horizontal acceleration when sliding downhill, set the relative horizontal acceleration of the sliding body = 0, and solve for the critical seismic coefficient of the unsaturated state.

[0025] Furthermore, in step S300, calculating the critical seismic coefficient corresponding to the accumulation body for the saturated state includes the following steps: S320 defines the horizontal length and vertical height of the saturated soil layer, as well as the initial total stress and initial effective stress perpendicular to the sliding surface, and calculates the normal and tangential forces of the saturated soil; where the normal force N s Calculated using the following formula: ; σ n ’Let L be the initial effective stress perpendicular to the slip surface, L be the horizontal length of the saturated soil layer, and θ be the dip angle of the slip surface. Tangential force T s Calculated using the following formula: ; σ n The initial total stress is perpendicular to the slip surface, and k is the horizontal seismic coefficient; S321, the expression is obtained through force analysis. Substituting the expressions for normal force and tangential force, the critical seismic coefficient for saturation state is obtained after simplification. Among them, the horizontal relative acceleration of the sliding body relative to the bedrock. g is the acceleration due to gravity. , φ The internal friction angle of the soil. φ ∗ The effective internal friction angle is considered after correction of the initial soil stress.

[0026] S400 uses the rectangular strip method of acceleration time history to integrate the time history of seismic acceleration exceeding the critical seismic coefficient piecewise, and obtains the permanent displacement of the sliding body corresponding to the unsaturated state and the saturated state, respectively.

[0027] Furthermore, step S400 includes the following steps: S410, the seismic wave acceleration time history is equivalent to the superposition of constant rectangular blocks with a time increment of Δt, and the acceleration within each block is constant; S420, initial stationary phase, application duration is... constant acceleration kg The integral is obtained t 0 Horizontal relative velocity at time and horizontal relative displacement ; and Satisfy the following formula: ; ; in, t 0 This is the initial time increment.

[0028] S430, subsequent phases ( Using the result of S420 as the initial value, the integral is obtained. t>t 0 horizontal relative velocity at time Relative displacement with respect to the horizontal μ ; ; ; Where t is the cumulative time; S440: Set the velocity of the sliding body to 0 when it stops, substitute the velocity expression to obtain the stopping time, and then substitute the displacement expression to obtain the final relative horizontal displacement in the unsaturated state. ; final relative horizontal displacement under saturation state ; Let be the horizontal relative displacement at time t=t0.

[0029] 1. Newmark method for unsaturated soil In this embodiment, in engineering practice, to evaluate the possibility of slope failure, the seismic coefficient (the ratio of ground acceleration to gravitational acceleration) is usually used to consider the seismic effect. Let the mass of the sliding body be M, the horizontal seismic coefficient be k, the inclination angle of the sliding surface be θ, and a thin layer of soil exist between the slider and the sliding surface. The friction coefficient between the slider and the sliding surface is μ = tanφ (φ is the internal friction angle). The seismic inertial force acts on the downslope direction, and when the slider slides downslope, its relative displacement along the sliding surface and its horizontal component are s and u (u = s × cosθ), respectively. The forces acting on the slider are as follows: Figure 2 As shown.

[0030] The normal component N and tangential component T of the force on the slider are respectively: (1) (2) Along the s-axis: (3) The relative horizontal acceleration u″ can be expressed as: (4) When the seismic inertial force acts on the uphill direction and the slider slides uphill: (5) When the slope angle θ is large, it is difficult for the slider to generate an upward relative displacement. For the accumulation slope in this embodiment, only equation (4) needs to be considered. When the slider is in the limit equilibrium state (T=μN), the corresponding horizontal seismic coefficient k is the critical seismic coefficient k. cr From equation (4), we can know that k cr =tan(φ-θ).

[0031] The above derivation is based on the assumption that the thin layer of soil between the slider and the sliding surface is cohesive. Considering the influence of cohesion *c*, let the density of the slider be *ρ*, its horizontal length be *L*, and its thickness be *ζ*. Then the mass of the slider is *M* = *ρLζ*. When the slider slides downwards, the anti-sliding force *R'* and the sliding force *T'* are respectively: (6) (7) Let R'=T', then the critical seismic coefficient k' considering the effect of cohesion can be obtained. cr : (8) Soil particles with a diameter d ≤ 0.075 mm are defined as fine particles, and their content is f. c ;f thre The threshold fine grain content is used to distinguish between soil skeleton structures that contain fine grains within sand and those containing sand within fine grains. When f c <f thre At that time, the soil skeleton is a "fine-grained sand" structure, and the presence of fine particles under cyclic loading does not affect the large strain characteristics of the soil. thre Defined as: (9) In equation (9), =D10 / D50; D10 and D50 are the particle sizes corresponding to 10% and 50% of the sand and fine-grained soil particles, respectively.

[0032] In this embodiment, the vibration table test model assembly D... 10 =0.040mm, D 50 =0.003mm, fine particle content f c =0.05. f is obtained from equation (9). thre =0.34, i.e., f c <f thre Therefore, the model test accumulation is a "fine-grained sand" skeleton structure. Studies on earthquake landslides show that the sliding surface material can be regarded as sand with very little fine grain content. In this case, the influence of cohesion on slope sliding can be ignored. Therefore, the calculations in the subsequent embodiments are still based on equation (4).

[0033] In fact, under the action of random seismic waves, the horizontal seismic coefficient k varies with time. In this case, the acceleration time history of the seismic wave can be considered as the superposition of rectangular blocks with a time increment of Δt, and k is constant within Δt. For example... Figure 3 As shown, when solving for the horizontal relative displacement u, the equivalent method described above can be divided into two stages: ① A constant rectangular acceleration of kg is applied to the slider initially at rest (t=0) for a duration of t=0~t0. Let the horizontal relative velocity and horizontal relative displacement at t=t0 be u0' and u0, respectively. Integrating equation (4) yields: (10) (11) ②When t>t0, kg=0. Substituting into equation (4), we get: (12) Taking equations (10) and (11) as initial values, and letting the horizontal relative velocity and horizontal relative displacement at t>t0 be u' and u respectively, we can integrate equation (12) to obtain: (13) (14) Let t1 be the time when the slider stops moving during this time period. At this time, u'=0. Substituting into equation (13), we get: (15) Substituting equation (15) into equation (14) yields the final relative horizontal displacement u1 of the slider (i.e., the horizontal component δ of the permanent displacement δ). r ): (16) Substituting equation (11) into equation (16), we get: (17) Equation (17) is the Newmark permanent displacement that occurs on the inclined straight sliding surface after the acceleration time history is divided into rectangular segments and then moved downhill.

[0034] 2. Newmark method for saturated soil The above embodiments are derived based on the unsaturated state of the sliding body. When the sliding body is saturated under rainfall conditions, the shear failure of the saturated soil caused by the earthquake often corresponds to undrained conditions. In this case, it can be considered that the change in pore water pressure in the saturated soil temporarily bears the seismic force perpendicular to the sliding surface.

[0035] like Figure 4 As shown, let the horizontal length and vertical height of the saturated soil layer be L and ζ, respectively, and the initial total stress and initial effective stress perpendicular to the sliding surface be σ. n and σ n ', then the normal force N of the saturated soil at this time s and tangential force T s They are respectively: (18) (19) From the force analysis, we can obtain: (20) Let M=ρLζ and σ n =ρgζcos 2 Substituting θ into equation (20) yields: ;(twenty one) Let tanφ* =μ((σ n ') / σ n )=((σ n ') / σ n If tanφ, then equation (21) can be simplified to: ;(twenty two) From equation (22), the critical seismic coefficient k when the sliding body is saturated can be obtained. cr,s =tanφ * -tanθ. The horizontal relative displacement u at time t=t0 can be obtained using the same analysis method as in the above embodiments. 0,s and the final relative horizontal displacement u of the sliding body 1,s They are respectively: ;(twenty three) ;(twenty four) S500, combining critical seismic coefficient and permanent displacement, analyzes the seismic stability of the accumulation body slope.

[0036] In this embodiment, the critical seismic coefficient is the "critical threshold" at which the slope begins to undergo permanent sliding. Its value is determined by mechanical and geometric parameters such as the shear strength (internal friction angle, cohesion), self-weight, and sliding surface inclination angle of the accumulation body (calculated separately for unsaturated and saturated states, denoted as k). c非饱 and k c饱 The larger the value, the stronger the slope's ability to resist earthquake forces (a greater earthquake acceleration is required to initiate sliding); the smaller the value, the more easily the slope becomes unstable during an earthquake.

[0037] Permanent displacement is the actual cumulative sliding distance of the sliding body during an earthquake (calculated separately for unsaturated and saturated states, denoted as δ). 非饱 and δ 饱 It directly reflects the scale and severity of the landslide. The greater the displacement, the more severe the damage after the slope becomes unstable (such as the extent of the landslide and the impact force).

[0038] The critical seismic coefficient determines whether slippage occurs (when the actual seismic coefficient of the ground motion k ≥ k). c Permanent displacement will only occur when k ≥ k; permanent displacement determines the "degree of harm of sliding" (even if k ≥ k c If the displacement is small, it may still be in an acceptable stable state.

[0039] Preliminary stability assessment based on critical seismic coefficient: For unsaturated regions: the maximum seismic coefficient (k) of the actual ground motion is used. max Calculated from the earthquake acceleration time history, k max =a hmax / g) and kc非饱 Comparison. If k max <k c非饱 This indicates that the area will not experience permanent slippage under seismic loading, and is therefore classified as "stable"; if k max ≥k c非饱 If it is determined to be "potentially unstable", further evaluation is required in conjunction with permanent displacement.

[0040] For the saturated region: Similarly, compare k max With k c饱 The initial judgment of "stable / potentially unstable" is completed (under saturation, due to the increase in pore water pressure, k...). c饱 Usually less than k c非饱 (It is more likely to enter a state of "potential instability").

[0041] Hazard assessment based on permanent displacement: For region k initially judged to be "potentially unstable" max ≥k c Introduce a recognized permanent displacement threshold from engineering practice (such as the "Technical Specification for Building Slope Engineering" or project experience value, usually taken as δ). cr =10~50cm: If δ < δ cr (such as the unsaturated region δ) 非饱 =3cm), which was judged as "slight sliding, basically stable" (the sliding scale is small and has limited impact on the overall structure of the slope).

[0042] If δ≥δ cr (such as the saturation region δ) 饱 =60cm), which is judged as "significant sliding, unstable" (the sliding scale is large and may cause overall damage).

[0043] Furthermore, the spatial distribution weight analysis of the overall stability judgment based on the two states and dual indicators can be combined with the spatial proportion of unsaturated and saturated areas under the influence of pre-earthquake rainfall (e.g., saturated areas account for 30% of the total slope area, and unsaturated areas account for 70%) to assign weights to the assessment results of different areas (the higher the area proportion, the greater the impact on overall stability).

[0044] Multi-scenario combination judgment: If both the unsaturated and saturated zones are deemed "stable," the overall slope is considered "earthquake-stable." If the unsaturated zone is "stable" but the saturated zone experiences "significant slippage" (and the saturated zone accounts for ≥30%), the overall slope is deemed "local instability leading to overall risk, unstable." If both the unsaturated and saturated zones experience "slight slippage" (total weighted displacement <δ), the slope is considered "earthquake-stable." crIf any region exhibits "significant slippage" and accounts for ≥50%, it is determined to be "overall instability and unstable".

[0045] The methods described in the above embodiments have at least the following beneficial effects: 1. Adapt to the actual mechanical properties of unsaturated soil and avoid parameter misjudgment: By defining the fine particle content (the proportion of soil particles with a particle size ≤ 0.075mm) and the threshold fine particle content, the soil skeleton structure of the unsaturated deposit is determined (such as the "fine particle in sand" structure). Combined with the conclusions of earthquake landslide research (the sliding surface material can be regarded as sand with low fine particle content), the influence of cohesion is ignored, so that the calculation of the critical seismic coefficient (derived based on stress analysis) is accurately matched with the shear resistance characteristics of unsaturated soil, avoiding the distortion of mechanical parameters caused by blindly introducing cohesion and improving the accuracy of critical state determination.

[0046] 2. Improve the dynamic accuracy of permanent displacement calculation: The "acceleration time history rectangular strip method" is adopted, which equates the seismic wave acceleration time history to the superposition of constant rectangular strips (the time increment is a constant value). It is divided into the initial static stage (t0 time period) and the subsequent stage (t>t0 time period). Based on the expression of relative horizontal acceleration, the relative velocity and relative displacement are calculated by piecewise integration. This can accurately capture the influence of acceleration changes at different time periods in the seismic motion time history on the motion state of the sliding body, avoid the neglect of time history details by traditional overall integration, and make the permanent displacement calculation of unsaturated sliding bodies more consistent with the actual sliding dynamic process.

[0047] 3. Laying the foundation for the correlation analysis of "rainfall-water content-stability": As an important component of the analysis of two states (unsaturated / saturated) of the accumulation body under the influence of pre-earthquake rainfall, the derivation of the Newmark method for the unsaturated state clarifies the calculation logic of the critical seismic coefficient and permanent displacement in this state. It complements the "Newmark method for saturated soil" and together solves the defect of the existing Newmark method in not distinguishing the water content of the soil. This enables the method to be specifically adapted to the stability assessment scenario of unsaturated accumulation bodies after pre-earthquake rainfall, and provides support for the overall improvement of the engineering practicality of the Newmark method.

[0048] Example 2: Based on the relevant results calculated in Embodiment 1 above, the following method for seismic stability analysis of accumulation slopes is provided, which includes the following steps: Q100 defines the core energy terms of the sliding body-slippery zone system, including the total energy of the seismic input system, the energy dissipated by the damping within the sliding body, the kinetic energy of the sliding body, the energy dissipated by friction, the energy dissipated by the slippery zone, and the decrease in the gravitational potential energy of the sliding body.

[0049] Furthermore, the total energy of the seismic input system is the total energy of the seismic input to the sliding body-slip zone system; the energy dissipation due to internal damping of the sliding body is the energy dissipation caused by internal damping of the sliding body; the kinetic energy of the sliding body is the energy possessed by the accumulation body due to sliding; the energy dissipation due to friction is the energy dissipation caused by friction between the sliding body and the surrounding medium during the sliding process; the energy dissipation due to slip zone is the accumulated strain energy generated by the softening of the weak layer between the sliding body and the bedrock due to strain; and the decrease in gravitational potential energy of the sliding body is the amount of decrease in gravitational potential energy during the sliding of the sliding body.

[0050] Q200, based on the principle of energy conservation, establishes the energy balance equation for the sliding body-sliding strip system.

[0051] Furthermore, step Q200 includes the following steps: Q210, Construct the original energy equation: Among them, E gr For the gravitational potential energy to decrease, E eq E is the total energy input to the sliding body-slip zone system for seismic motion. ’ eq For the energy dissipated by the damping within the sliding body, E k E is the kinetic energy of the sliding body. f For energy dissipation due to friction, E slip This represents the cumulative strain energy of the sliding belt.

[0052] Q220, order The energy balance equation of the sliding body-sliding strip system is obtained. Among them, E * eq For the equivalent seismic input energy, E dp This represents the energy dissipated by the external damping of the system.

[0053] Let the energy of the seismic input to the sliding body-slip zone system be E. eq For soil, the heat and sound energy generated during deformation are negligible. Consider the energy dissipation (internal damping energy dissipation) E of soil under seismic load due to internal damping. eq When the sliding body does not undergo permanent displacement, the input seismic energy will be completely converted into internal damping energy dissipation without causing any other energy changes. When the sliding body undergoes permanent displacement, E eq -E eq 'and gravitational potential energy decrease E' gr The kinetic energy E converted into the sliding body k and external damping energy dissipation E dp Due to friction within the soil, the landslide actually slides along the slip zone rather than the slip surface. Furthermore, during an earthquake-induced landslide, as seismic waves are transmitted from the bedrock through the slip zone to the landslide body, the energy changes in the landslide system caused by the seismic motion must be reflected in the strain energy of the slip zone. Let the cumulative strain energy of the slip zone be E. slip (Usually manifested as energy consumption), frictional energy consumption is Ef The energy of the sliding body-sliding strip system can be expressed as: (25) make Then equation (25) can be simplified to: (26) In existing technologies, the energy dissipation E of the sliding belt is not explicitly defined. slip and external damping dissipation energy E dp To differentiate, and to consider the internal damping energy dissipation E eq It can be ignored.

[0054] The instability of accumulation slopes under seismic loading is often sudden, making it very difficult to measure permanent displacement during the sliding process. Furthermore, in practical engineering, the permanent displacement of seismic slopes is not easily obtained. On the other hand, when permanent displacement (or E) occurs... k A value greater than 0 usually indicates that the slope has become unstable and failed.

[0055] Q300, calculate the specific values ​​of each energy term in step Q100 respectively.

[0056] Furthermore, step Q300 includes the following steps: Q310, Calculate the decrease in gravitational potential energy of a sliding motion device. Where M is the total mass of the sliding body, g is the acceleration due to gravity, and δ r Let θ be the horizontal relative displacement of the sliding body, and θ be the inclination angle of the sliding surface.

[0057] Q311, Calculate the energy dissipation of external damping. .

[0058] Q312, Calculate the energy consumption E of the sliding belt. slip = Where α is the bedrock dip angle, and η is the peak displacement of the shear stress-displacement curve.

[0059] Furthermore, the energy dissipation due to damping within the sliding body. ; The total energy E of the seismic input system eq =WW d W represents the total energy of the seismic waves. d This refers to the energy dissipated during the propagation of seismic waves.

[0060] 1. External damping energy dissipation Based on the method in Example 1, during the process of generating a relative horizontal displacement u0 (0~t0), the dissipated energy E 1 dp for: (27) The relative horizontal displacement is from u0 to δ r During the process (t0~t1), the energy dissipated is E 2 dp for: (28) During the entire process of the slider generating relative displacement (0~t1), the energy dissipated is E. dp for: (29) k cr =tan(φ-θ), μ=tanφ and equation (17) are substituted into equation (29) to obtain: (30) When the sliding body is saturated: ;(31)

[0061] 2. Seismic energy that drives the sliding body to slide When performing energy assessment, it is necessary to know δ or δ r This means the sliding body has stopped moving. When the sliding body stops moving, let E in equation (26) k =0 yields: (32) At this point, the gravitational potential energy of the sliding body decreases to: (33) Substituting equations (30) and (33) into equation (32), we get: (34) When the sliding body is saturated: ;(35)

[0062] 3. Energy dissipation of the sliding belt Mountainous landslides typically occur along existing or potential slip surfaces, which mechanically exhibit strain softening properties. Furthermore, there may be resisting sections on the slip zone due to the uplift of underlying bedrock; the soil and rock in these sections may exhibit strain hardening properties. When the length of the strain hardening section is much greater than the length of the strain softening section, the slope usually exhibits good stability. The following analysis assumes that the length of the strain hardening section on the slip zone is very small, considering only the scenario where strain softening occurs on the slip zone.

[0063] For strain-softening media, the shear stress τ s The Weibull distribution can be described as follows: (36) In equation (36), G0 is the initial shear modulus; δ is the permanent displacement of the sliding band; η is the peak displacement of the shear stress-displacement curve; h is the thickness of the sliding band; and n is the shape parameter of the shear stress-displacement curve.

[0064] Let the sliding surface length of the strain-softening medium be l. s Then the cumulative strain energy of the sliding belt is: (37) Integral equation (37): (38) In equation (38), Γ represents the Gamma function.

[0065] When considering the influence of n, the cumulative strain energy of the sliding belt is relatively accurate, but its integral result is quite complex, making it impossible to obtain the specific E. slip The larger the value of n, the greater the homogeneity of the soil and rock material, the steeper the τ-(δ / η) curve, and the higher the peak value. If the influence of the coefficient n is ignored, taking n=1 (i.e., the negative exponential model) yields: (39) Usually η≪δ, taking the limit of equation (39), we get: (40) like Figure 5 As shown, with the increase of permanent displacement δ, E slip Ultimately tending towards G0l s η 2 / h. Furthermore, the above energy expression is described using permanent displacement δ, thus encompassing deformation characteristics under different time-dependent shear stress levels. The value of the slip band thickness h will affect E. slip The calculation results are affected, and existing technology research shows that: (41) , (r≤1); (42) In equations (41) and (42), Mg is the sliding gravity; G e The shear modulus of the strain-hardening medium; l e α represents the length of the strain-hardened section; α represents the bedrock dip angle.

[0066] According to this embodiment, l e →Assuming 0, we have r=0. Substituting into equation (41), we get: (43) Substituting equation (43) into equation (40), we get: (44) Ring shear tests can effectively simulate the dynamic response of sand along the sliding surface under seismic loading. The peak shear displacement corresponding to the typical shear stress-displacement curve of sand is around 1.0 × 10⁻⁶. -3 Around m, take η = 1.0 × 10 -3 Substituting m into equation (44), we get: ;(45)

[0067] 4. Equivalent friction coefficient and equivalent slip surface During the sliding process of a landslide under seismic loading, friction between the soil / rock mass and the bedrock surface is one form of energy dissipation. Furthermore, the dynamic prediction of long-distance landslides also requires the measurement of basement friction. Based on past debris flow landslides, existing techniques employ the concept of equivalent friction coefficient to study the statistical relationship between the equivalent friction coefficient or the maximum travel distance of the debris flow and its volume. However, these statistical relationships are difficult to reflect the geological environment of individual debris flows, leading to significant calculation errors. The influence of numerous factors on volume friction is also difficult to consider in detail. Additionally, some studies have derived the relationship between the long-distance travel distance of debris flows and the potential energy of the debris volume based on rigid body theory, without considering the energy dissipation of the debris flow; however, this is only applicable to debris flows in rock landslides.

[0068] In existing technology, it is believed that the frictional force at the soil-bedrock interface can be measured by the seismic waves radiated by the landslide, and that the effective force system of the source-time function is a horizontal force. Furthermore, the horizontal force during the landslide's movement is correlated with a wave of amplitude F. P The sinusoidal source-time function is considered equivalent, and it is believed that combining the two source-time functions can provide empirical corrections for the complex time-varying properties and non-rigid body motion of the sliding body. The drawback of this solution method is that it not only requires complex artificial seismic wave synthesis but also necessitates finding the F corresponding to the actual observed displacement. P The solution process is quite complex. However, this method also provides a useful reference for solving the equivalent friction coefficient μ': by combining the friction theory based on rigid bodies with the actual sliding displacement, a relatively accurate value of μ' can be obtained.

[0069] If the horizontal force corresponding to the actual observed displacement is considered as the seismic inertial force, then the key to the rigid body energy principle reflecting the continuous deformation of sand slopes lies in inverting the equivalent friction coefficient based on the actual sliding displacement and frictional energy dissipation. Let δ be the actual sliding displacement of the sliding body (its horizontal component is δ). r =δcosθ), μ' is the equivalent friction coefficient during the sliding process, and the gravitational potential energy drop E gr and the seismic energy E that drives the sliding body to slide eq * If the dissipation is entirely due to the component of gravity Mgcosθ, then: (46) Substituting equations (32) to (34) into equation (46), we get: (47) When the soil is saturated, according to equations (31) and (35), we get: (48) When considering the energy dissipation effect of internal damping, the non-rigid motion of the sliding body has actually been corrected from an energy perspective. For example... Figure 6 As shown, for the case where the sliding surface is not a straight line, let the initial center of gravity of the sliding body be P, the center of gravity of the sliding body after it finally stops moving be Q, and the horizontal sliding distance be... The overall tilt angle of the sliding body before and after sliding is θ. If we consider it as the average dynamic friction coefficient during the sliding process, then the case based on a straight slip surface can be equivalent to a non-linear slip surface. From equation (47), we can see that the normalized seismic energy... This is equivalent to raising the center of gravity of the unsaturated sliding body from P to P', corresponding to The equivalent slip surface is P'Q, corresponding to According to equation (48), for a saturated sliding body, the normalized seismic energy is... The corresponding elevation of the center of gravity Equivalent slip surface corresponding .

[0070] Q400 verifies whether each energy term satisfies the energy balance equation, and analyzes the seismic stability of the accumulation body slope by combining the proportional relationship between energy terms.

[0071] Furthermore, the method also includes the following steps: S500, combining the horizontal component of the actual sliding displacement of the sliding body with the frictional energy consumption, calculates the equivalent friction coefficient of the pair under unsaturated state and the equivalent friction coefficient under saturated state.

[0072] In an exemplary embodiment, a model test was conducted on the above method. In model test one, all soil in the failure zone slid down and accumulated in a triangular pattern at the toe of the slope. At this time, the slope angle of the slid body was approximately 33.7°, and the volume was approximately 5.28 × 10⁻⁶. -3 m 3 (Approximately 9.44% of the volume of the test stack); According to the second theorem of similarity, the geometric similarity ratio C is taken. l =36 calculations indicate that the equivalent volume of the slope slippage of the prototype accumulation body in the model test is approximately 0.19m³. 3 Therefore, the landslide disaster caused by Model Experiment 1 was quite limited. Furthermore, the collapse of loose deposit slopes shown in Model Experiment 2 was the main failure mode triggering large landslides in the Wenchuan earthquake. In this embodiment, Model Experiment 2 was used as the basis for verifying the energy equation, such as... Figure 7As shown.

[0073] ①E gr E * eq E dp E slip and E f Solving Using the intersection of the model box's bottom plate and rear wall as the origin, the accumulated mass is considered homogeneous before and after failure, with a combined surface of triangles and trapezoids in cross-section. Based on the principle of centroid calculation for homogeneous composite shapes, the initial centroid coordinates of the accumulated mass are P (41.88cm, 48.11cm), and the centroid coordinates after sliding are Q (63.09cm, 33.80cm). Based on the measured results of the model test, δ... r =21.21cm, and the overall tilt angle of the sliding body before and after sliding is θ=34.01°.

[0074] After the rainfall in the second model test, the mass of the accumulated material was M = 81.23 kg, and the gravitational acceleration was taken as g = 10 m / s². 2 , will δ r Substituting =0.21m and θ=34.01° into equation (33), we can obtain the gravitational potential energy drop E. gr =114.29J; internal friction angle of loose aggregate =36.20°, substituting into equation (34) yields the seismic energy E that drives the sliding body to slide. * eq =6.52J.

[0075] E gr =114.29J and E * eq Substituting 6.52J into equation (30), we can obtain the external damping energy dissipation E. dp =120.81J. Due to the limitations of the steep and rough base surface, the failure of the loose accumulation model test in this embodiment showed a shear zone in the soil layer at the toe of the slope. However, due to the sudden occurrence of the landslide, it was difficult to determine the specific location of the shear zone. Considering that when the base surface is steep, the slope of the accumulation mainly slides down along the base surface as a whole, when calculating the energy dissipation of the sliding zone, the mass of the soil on the upper sliding surface is M1=52.64kg, the inclination angle is α1=60°; the mass of the soil on the lower sliding surface is M2=28.59kg, the inclination angle is α2=40°. Substituting into equation (45), the energy dissipated by the sliding zone after the sliding is E. slip =1.61J. Therefore, E f =119.20J.

[0076] ② and E eq Solving In existing technologies, the assessment of soil energy dissipation is based on undrained cyclic shear tests of saturated or highly saturated soil samples, making it difficult to assess the energy dissipation of unsaturated soil under seismic loading. Furthermore, seismic wave energy is primarily provided by P-waves, SH-waves, and SV-waves, and wave transmission, reflection, refraction, waveform distortion, and transformation occur at the rock-soil interface, resulting in a highly complex seismic wave field. In practical slope engineering, the damping energy dissipation of soil and rock masses is difficult to calculate quantitatively; therefore, this embodiment focuses on E... * eq The calculations use statistical ratios from actual earthquake-induced landslide surveys. In existing technology, survey statistics indicate that the seismic energy driving a landslide is approximately 0.25 times the seismic energy entering the landslide system, i.e.: (49) E * eq Substituting 6.52J into equation (49), we can obtain the seismic energy E entering the sliding body-slip zone system. eq =26.08J. Therefore, the energy dissipated by the internal damping of the sliding body is... .

[0077] ③ Input the seismic energy of the model slope Traditional seismic energy definition requires knowledge of the wave impedance and vibration velocity of the soil and rock mass near the earthquake source. However, in model tests, the direct source of seismic energy is the shaking table, making traditional seismic energy definition inapplicable. Currently, seismic wave energy calculations are mainly performed using analytical methods based on stress wave propagation theory and numerical simulations. However, these two methods have various shortcomings that hinder practical application. In geotechnical dynamics, the attenuation of elastic waves during propagation in soil and rock media is a crucial property of these materials. To avoid complex elastic wave propagation calculations while reflecting the attenuation properties, this embodiment uses the seismic wave quality factor Q, commonly used in geophysics, to characterize this attenuation. (50) In equation (50), W and W d These represent the total energy of the seismic wave and the energy dissipated during its propagation, respectively.

[0078] Let the bedrock damping ratio be λ. br , λ br The relationship with Q is: (51) By combining equations (50) and (51), we can obtain: (52) The difference in wave impedance between bedrock and soil leads to different distributions of seismic energy. Taking the bedrock damping ratio λ... br =5%, W can be obtained according to formula (52).d / W≈0.63. Let the total energy of the seismic wave W be divided by the energy dissipated by the bedrock. d In addition, the remaining energy is entirely contributed to the sliding body-sliding strip system, that is: (53) Besides reflection at the rock-soil interface and dissipation in the bedrock, 30% to 40% of the seismic energy propagates upwards and reaches the upper soil layers. Therefore, it is appropriate to use equation (53) to estimate the energy entering the landslide-slip zone system. E eq Substituting =26.08J into equation (53), we can obtain the seismic energy of the input model slope as W=70.49J.

[0079] In one exemplary embodiment, based on existing model tests, the energy changes of an accumulation slope containing weak interlayers and an arc-shaped slip zone during the failure process are verified.

[0080] The density of the packing material in the model test was ρ1 = 1908 kg / m³. 3 (Take g = 10 m / s) 2 The cohesion is c1 = 1.55 kPa, the internal friction angle is 37.9°, and the volume is V = 1.079 m³. 3 The mass is M=2058.73kg, the main material is river sand, the moisture content is 3.29%, and the porosity is calculated to be 0.38 based on the soil particle specific gravity Gs=2.65. The accumulator is densely packed. The weak interlayer is also mainly composed of river sand, with a density of ρ2=1720kg / m³. 3 The cohesion c2 = 0.27 kPa, and the internal friction angle = 41.7°; the bedrock material is mainly composed of clay with a density of ρ3 = 2206 kg / m³. 3 The cohesion c3 = 43 kPa, and the internal friction angle = 38.91°. The weak interlayer is arc-shaped and 5 cm thick; the slope angle of the accumulation body is 50°, and the dimensions of the entire model slope are as follows. Figure 8 As shown.

[0081] In the model test, the entire soil layer was unsaturated, and the applied seismic waves were Wenchuan waves, Kobe waves, and EL-Centrol waves with peak ground accelerations of 0.1g, 0.2g, 0.4g, 0.5g, 0.6g, and 0.7g, respectively. When a 0.2g Wenchuan wave was applied, the landslide began to loosen; at 0.4g, the top of the landslide cracked; at 0.5g, extensive cracking occurred on the surface of the landslide, and the landslide progressed along the weak interlayers towards the toe of the slope; at 0.6g, the entire landslide slid, and landslide failure occurred. The outline of the collapsed deposit is shown in the figure. Figure 8 As shown.

[0082] The original centroid coordinates of the deposit were P (113cm, 90cm), and after the overall collapse, the centroid coordinates were Q (107.8cm, 86.7cm). The permanent horizontal displacement was δ. r =5.2cm, the overall tilt angle of the sliding body before and after sliding is θ=32.40°. Gravitational potential energy decrease E gr =679.36J, the seismic energy E that drives the sliding body to slide. * eq =103.09J, external damping energy dissipation E dp =782.45J, internal damping energy dissipation E eq =309.27J, the energy of the sliding body-slip zone system and the seismic energy of the input model slope are respectively E eq =412.36J and W=1114.49J. Taking the elastic modulus of dense sand as E=46MPa and Poisson's ratio μ=0.25, its shear modulus can be calculated to be 18.4MPa; due to the deterioration of the soil during the dynamic process, its shear modulus before the landslide is very low, and the calculation of the energy dissipation of the slip zone requires the shear modulus before the landslide failure. In this embodiment, G0=1.84MPa is taken. The arc length of the sliding surface is l s =2.0m, h=0.05m and η=1.0×10 -3 Substituting m into equation (40), we can obtain E. slip =73.60J, therefore E f =708.85J.

[0083] The model test results in this embodiment and existing model tests show that internal damping energy dissipation cannot be ignored and must be considered in the energy equation. The energy equation proposed in this embodiment can better reflect the influence of landslide deformation energy dissipation and has certain guiding significance for the study of the stability of other types of sedimentary bodies. In addition, to reduce the impact of landslide deformation energy dissipation on slope stability, engineering measures such as anti-slide piles and geotechnical reinforcement can be adopted.

[0084] In the model experiment of this embodiment, E slip / E dp =0.013; Taking the peak value of the shear stress-displacement curve of the sliding surface soil of the Donghekou landslide as an example, η = 5.0 × 10 -3 m, we can get E slip / E dp =0.067, meaning that the energy dissipated by the sliding belt accounts for a very small proportion of the energy dissipated by the external damping.

[0085] Although it can be assumed that the shear stress at all points on the slip surface reaches its peak shear strength simultaneously within a very short time at the instant a strong earthquake triggers a landslide, the stress-strain curves of the soil elements in the slip zone will exhibit different shapes or different degrees of softening due to differences in the stress conditions of the soil elements on the slip surface and other environmental factors. To obtain E...slip In this embodiment, n=1 is used for the integral result, which implicitly assumes that the stress-strain curves of all soil elements in the slip zone have the same shape or the same degree of softening. Furthermore, this paper assumes that the length of the resisting segment is negligible. If a finite-length resisting segment exists on the slip surface, the strain hardening energy dissipation of the soil in the resisting segment should also be included in the slip zone energy dissipation term. These assumptions may lead to a certain degree of ambiguity regarding E. slip The underestimation.

[0086] The model test of the loose deposit slope example in this paper yielded an equivalent friction coefficient μ' = 0.71, tanθ = tan34.01° = 0.67. From equation (47), it can be seen that to accurately evaluate μ', the value of tan(φ-θ) is also required; here, θ = 34.01° is still taken. Based on the parameter values ​​provided by existing technology, if the deposit is composed of angular gravel and red clay, then... φ =35.68°; if it is a landslide at the contact surface of gravelly soil and bedrock, take φ =38.78°; if it is the slope of the reservoir bank deposit after water storage, take φ =35.0°, the corresponding tan(φ-θ) values ​​are 0.029, 0.083, and 0.017, respectively, all smaller than 0.67. For existing model tests, μ'=0.73; tan(φ-θ)=0.096, also smaller than tanθ=0.63. Therefore, for the slope of the accumulated mass with a steep inclination angle, the overall inclination angle θ before and after the sliding mass is the dominant factor of the equivalent friction coefficient μ'.

[0087] The methods described in the above embodiments have at least the following beneficial effects: 1. Comprehensive coverage of system energy composition, significantly improving the accuracy of stability analysis. Traditional methods often neglect the energy dissipation due to sliding body deformation (internal damping) and the energy dissipation due to slip zone (strain softening), simplifying the energy process with only "rigid body sliding," leading to errors in energy calculation. This new method, however, constructs an energy balance equation based on the sliding body-slip zone system, comprehensively incorporating six major energy terms: total seismic input energy, internal damping energy dissipation (dissipation due to sliding body deformation), frictional energy dissipation (dissipation due to sliding body friction), slip zone energy dissipation (cumulative dissipation due to slip zone strain softening), gravitational potential energy reduction (energy released by the lowering of the sliding body's center of gravity), and kinetic energy, achieving "no omissions in energy balance." For example, the document verifies through shaking table tests that internal damping energy dissipation accounts for 13.9% to 28.3% of the total dissipated energy in the sliding body-slip zone system. Although the slip zone energy dissipation is small, it is not negligible. This comprehensiveness avoids "overestimation of stability" caused by missing energy terms (such as the misjudgment of slope stability when traditional methods ignore internal damping), making the analysis results more consistent with the actual dynamic response of the soil.

[0088] 2. Adaptable to complex slip surfaces and water content conditions, significantly expanding the applicability of the method. On the one hand, traditional methods lack a unified equivalent scheme for common non-linear slip surfaces (broken lines, arcs) in embankments. This method, based on energy principles, uses "center of gravity change + equivalent friction coefficient inversion" to convert non-linear slip surfaces into linear ones. It uses the horizontal displacement of the center of gravity and the overall tilt angle before and after the slip surface to determine the equivalent friction coefficient by combining gravitational potential energy drop and friction energy dissipation. This allows for accurate calculation of energy distribution without simplifying the slip surface geometry, solving the problem of quantitative analysis difficulties for arc-shaped and broken-line slip surfaces. On the other hand, this method can couple the soil moisture content differences caused by pre-earthquake rainfall: in the unsaturated state, the soil skeleton structure is determined by the fine-grain content threshold, correcting the internal friction angle; in the saturated state, the influence of pore water pressure on effective stress is considered, deriving energy dissipation formulas for different states. This avoids the traditional method's "one-size-fits-all" approach that ignores the moisture content state, making it suitable for embankment slope analysis in various scenarios such as rainy mountainous areas and reservoir banks.

[0089] 3. Quantify energy decay and dissipation distribution to support precise engineering decisions. Traditional methods often directly use seismic ground acceleration time histories, neglecting energy attenuation during seismic wave propagation (such as bedrock dissipation), leading to an overestimation of input energy. This method introduces a seismic wave quality factor Q, correlating the Q value with the bedrock damping ratio to quantify the attenuation process of seismic waves from the source to the sliding body-slip zone system. This allows for accurate back-calculation of the total seismic energy of the input model slope, making the energy input calculation more closely reflect actual propagation patterns. Simultaneously, this method can output the proportion of each energy term (e.g., internal damping energy consumption accounts for 13.9%, and friction energy consumption accounts for 84.9% in the document model test), identifying "key energy consumption areas" (such as concentrated slip zone energy consumption areas and saturated areas with significant internal damping energy consumption). This provides targeted directions for engineering reinforcement—for example, using anti-slip piles to enhance the shear capacity of the slip zone in concentrated energy consumption areas, and adding drainage systems to reduce pore water pressure in saturated areas with high internal damping energy consumption. This avoids the "blindness" of traditional reinforcement methods and improves the effectiveness and economy of engineering measures.

[0090] 4. Couple "stability assessment and hazard quantification" to achieve full-chain evaluation. Traditional methods often rely solely on "critical acceleration" to determine "instability," failing to quantify the severity of the resulting damage. This new method, based on energy balance, assesses slope instability by determining if "total energy exceeds total dissipated energy" (total energy = energy input to the system + gravitational potential energy drop = total dissipated energy + kinetic energy; kinetic energy is zero when the slide stops). It also quantifies the scale of instability through "gravitational potential energy drop and slip zone energy consumption"—for example, a greater gravitational potential energy drop indicates a greater drop in the slide's center of gravity, resulting in a larger sliding distance and impact force; higher slip zone energy consumption indicates more severe slip zone deformation and more complete slope damage. This coupled assessment of "instability probability + severity" provides a more comprehensive stability rating (e.g., "minor instability - moderate hazard" and "severe instability - high hazard"), offering a more scientific basis for slope seismic risk classification and management (e.g., evacuation zone delineation and emergency reinforcement priority).

[0091] In summary, this method effectively overcomes the limitations of traditional methods by "covering all energy elements, adapting to complex scenarios, providing quantitative decision support, and evaluating the entire chain," and is more in line with the complex mechanical nature of the seismic response of embankment slopes, providing a more accurate and practical stability analysis tool for engineering practice.

[0092] Furthermore, although the steps of the method in this disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps may be omitted, multiple steps may be combined into one step, and / or a step may be broken down into multiple steps.

[0093] While specific embodiments of the invention have been described in detail by way of examples, those skilled in the art should understand that the examples are for illustrative purposes only and are not intended to limit the scope of the invention. Those skilled in the art should also understand that various modifications can be made to the embodiments without departing from the scope and spirit of the invention.

Claims

1. A method for seismic stability analysis of accumulated slopes based on an improved Newmark method, characterized in that, The method includes the following steps: S100, if the potential sliding surface of the bedrock overlying deposits is a straight surface, then the potential sliding surface of the bedrock overlying deposits is treated in the conventional way; if the sliding surface is not a straight surface, then the sliding surface is equivalent to a straight sliding surface based on the energy principle. S200, based on the impact of pre-earthquake rainfall, divides the deposits into unsaturated and saturated states; S300 calculates the critical seismic coefficients for the accumulation body under unsaturated and saturated conditions, respectively. S400 uses the rectangular strip method of acceleration time history to integrate the time history of seismic acceleration exceeding the critical seismic coefficient piecewise to obtain the permanent displacement of the sliding body corresponding to the unsaturated state and the saturated state, respectively. S500, combining critical seismic coefficient and permanent displacement, analyzes the seismic stability of the accumulation body slope.

2. The seismic stability analysis method for accumulated slopes based on the improved Newmark method according to claim 1, characterized in that, The method of equating the sliding surface to a straight sliding surface based on the energy principle includes the following steps: S110, determine the initial center of gravity of the sliding body before sliding and the final center of gravity after sliding; S120, combining the horizontal sliding distance of the sliding body and the overall tilt angle before and after sliding, constructs an equivalent straight sliding surface that matches the energy of the actual sliding process.

3. The seismic stability analysis method for accumulated slopes based on the improved Newmark method according to claim 1, characterized in that, In step S300, for the unsaturated state, the calculation of the critical seismic coefficient corresponding to the accumulation body includes the following steps: S310 defines soil particles with a diameter ≤ 0.075 mm as fine particles, and calculates the fine particle content f. c ; S311, if f c <f thre Then the soil skeleton of the accumulation body is determined to be sand with fine-grained structure; f thre This is the threshold for fine particle content; ； in, =D10 / D50; D10 and D50 are the particle sizes corresponding to 10% and 50% of the sand and fine-grained soil particles, respectively. S312, analyze the normal and tangential forces of the sliding body under seismic load, derive the expression for the relative horizontal acceleration when sliding downhill, set the relative horizontal acceleration of the sliding body = 0, and solve for the critical seismic coefficient of the unsaturated state.

4. The seismic stability analysis method for accumulated slopes based on the improved Newmark method according to claim 1, characterized in that, In step S300, calculating the critical seismic coefficient corresponding to the accumulation body for the saturated state includes the following steps: S320 defines the horizontal length and vertical height of the saturated soil layer, as well as the initial total stress and initial effective stress perpendicular to the sliding surface, and calculates the normal and tangential forces of the saturated soil; where the normal force N s Calculated using the following formula: ； σ n ’ Let L be the initial effective stress perpendicular to the slip surface, L be the horizontal length of the saturated soil layer, and θ be the dip angle of the slip surface. Tangential force T s Calculated using the following formula: ； σ n The initial total stress is perpendicular to the slip surface, and k is the horizontal seismic coefficient; S321, the expression is obtained through force analysis. Substituting the expressions for normal force and tangential force, the critical seismic coefficient for saturation state is obtained after simplification. Among them, the horizontal relative acceleration of the sliding body relative to the bedrock. g is the acceleration due to gravity. , φ The internal friction angle of the soil. φ ∗ The effective internal friction angle is considered after correction of the initial soil stress.

5. The seismic stability analysis method for accumulated slopes based on the improved Newmark method according to claim 4, characterized in that, Step S400 includes the following steps: S410, the seismic wave acceleration time history is equivalent to the superposition of constant rectangular blocks with a time increment of Δt, and the acceleration in each block is constant; S420, initial stationary phase, application duration is... constant acceleration kg The integral is obtained t 0 Horizontal relative velocity at time 1 and horizontal relative displacement ; and Satisfy the following formula: ； ； in, t 0 This is the initial time increment; S430, subsequent phases ( Using the result of S420 as the initial value, the integral is obtained. t>t 0 horizontal relative velocity at time Relative displacement with respect to the horizontal μ ; ； ； Where t is the cumulative time; S440: Set the velocity of the sliding body to 0 when it stops, substitute the velocity expression to obtain the stopping time, and then substitute the displacement expression to obtain the final relative horizontal displacement in the unsaturated state. ; final relative horizontal displacement under saturation state ; Let be the horizontal relative displacement at time t=t0.

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